Small groups, large profits: Calculating interest rates in community-managed microfinance Ole Dahl Rasmussen Savings groups are a widely used strategy for women’s economic resilience – over 80 per cent of members worldwide are women, and in the case described here, 72.5 per cent. In these savings groups it is common to see the interest rate on savings reported as ‘20–30 per cent annually’. Using panel data from 204 groups in Malawi, I show that the correct figure is likely to be at least twice as much. For these groups, the annual return is 62 per cent. The difference comes from sector-wide application of non-standard interest rate calculations and unrealistic assumptions about the savings profile in the groups. As a result, it is impossible to compare returns in savings groups with returns elsewhere. Moreover, the interest on savings cannot be compared with the interest rate on loans. I argue for the use of a standardized comparable metric and suggest easy ways to implement it. Development of new tools and standards along these lines are fortunately under way from key players in the sector and should be welcomed by donors, politicians, and practitioners to improve transparency and monitoring. Keywords: microfinance, interest rates, performance monitoring, community-managed microfinance, village savings and loan associations, Malawi, NGO In 2011 the weekly newspaper The Economist called savings groups ‘the hottest trend in microfinance’ and wrote: ‘returns on savings are extremely high – generally 20–30 per cent a year. Borrowers typically pay interest rates of 5–10 per cent a month’. In this paper I demonstrate how savings groups enable some of the poorest Africans to earn not 30 per cent, but 60 per cent interest on their savings. I do this by applying the most widely used financial calculation of interest rates to panel data on 204 savings groups with 3,544 members in Malawi, finding the median interest on savings to be 62 per cent per year, or 3.8 per cent per month. This figure is directly comparable to the 10 per cent monthly interest rate on loans.

Ole Rasmussen ([email protected]) is an adviser on Evaluation and Microfinance for DanChurchAid and a PhD student at University of Southern Denmark. The author would like to thank CARE Malawi for providing the data, Hugh Allen for continuous feedback, Nikolaj Malchow-Møller for comments on an earlier draft, Knud Rasmussen for helpful insights and two anonymous referees for useful suggestions. The opinions expressed in this article are the personal views of the author which are not necessarily the views of CARE International. © Practical Action Publishing, 2012, www.practicalactionpublishing.org doi: 10.3362/1755-1986.2012.030, ISSN: 1755-1978 (print) 1755-1986 (online) December 2012

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The paper discusses an argument against the standard financial calculation of interest The proposed calculation can be used to spot groups in trouble

The discussion is important because the current calculation makes interest rates on savings incomparable to the interest rate on loans as well as to interest rates elsewhere. De Mel et al. (2008) have shown that returns in Sri Lankan microenterprises are 60 per cent. If it were true that savings groups generate only 30 per cent, Sri Lankan savers should keep their money in microenterprises and not join savings groups. But in finding that savings groups generate returns of 60 per cent, the case is different. De Mel et al. do not provide information on savings alternatives in Sri Lanka, but the imagined example illustrates why the difference matters. It is no coincidence that transparent pricing is at the core of current efforts to ensure client protection in microfinance: people should know what they pay, and also what they get. Finally, non-standard interest rate calculations make monitoring difficult: when loans and savings are not comparable, how do we know the good groups from the bad ones? Savings groups have at least 1.5 million members worldwide, primarily in Africa. Since more than 80 per cent of members worldwide are women (72.5 per cent in the case described here), the topic is particularly relevant to discussions on women’s economic resilience. If the savings groups reporting on the portal http://savingsgroups.com were a single microfinance institution, this institution would be the ninth largest in the world and the second largest in Africa with regard to total number of savers. In the next two sections, I discuss a relevant argument against the standard financial calculation of interest: the fact that interest rates in general, and compounded interest in particular, are alien to most cultures where savings groups thrive. After a general discussion of interest rate calculations, I turn to data and analyse the interest rate in 204 Malawian savings groups, each observed four times during one year. I also develop a look-up table that enables use of the standard financial calculation with very little computation. After this, I provide an example of how the new interest rate metric can be used to monitor groups. Since the proposed calculation enables direct comparison of interest rates on loans and on savings, the difference between these two can be used to spot groups in trouble – something project managers can use to direct attention to the right places. Apart from the positive message that interest rates on savings are twice as high as we thought, my primary recommendation is to acknowledge the advantages of the standard financial calculation as described in Annex 1. In situations where we cannot use this calculation, we should at least use the best possible approximation. Fortunately, the leading provider of monitoring tools for savings groups, VSL Associates, has decided to change its calculations, taking some, though not all, of these issues into account in the tools currently being developed. As such, the present paper serves to justify

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why this change is needed and why it should be adopted by the rest of the savings group sector.

Are savings groups different? Savings groups are groups of 15 to 25 people, the majority women, who are taught how to manage their own funds. Their precise way of working is carefully described elsewhere (Allen and Panetta, 2010), but typically savings are made on a regular basis (e.g. weekly) and the saved capital is lent to the group members. Loan duration is commonly three months and all the groups’ assets are shared out once every year or so according to the individual level of savings. These groups are usually not regulated, and people working with savings groups commonly refer to them as being ‘under the radar’ of national supervision. Some perceive this as an advantage, whereas others point out that groups under the radar can avoid legislation which requires them to provide information to consumers, in particular the interest rates on loans and savings (Rhyne and Rippey, 2011). Partly because of this, interest rate calculations have not followed the standards and practices used elsewhere. In the next section I will discuss why I think that standard financial calculations should be followed, even for savings groups.

To compound or not to compound

Anthropologists suggest that the concept of interest rates originated in the countries that are today donors of foreign aid

December 2012

The history of interest is long: Greece in 600 BC and Babylon 1,200 years earlier had interest rates and legislations regulating them. Nevertheless, research in anthropology suggests that the concept of interest rates originated in the countries that are today donors of foreign aid (Homer and Sylla, 1996). As a result, the concept might be alien to most savings group members. Certainly, compounded interest is an intrinsic part of the culture of finance in many high GDP countries, so much so that the method I propose below is not just used in most textbooks on finance, but has also been made into law in many jurisdictions, including the EU and USA (Truth in Savings Act 1991; EU Directive 2008/48/EC; Brown and Zima, 2011; MFTransparency, 2011). What is so special about compounded interest? It multiplies at an ever-increasing rate. If I invest 100 shillings for two months and get 225 shillings at the end of the period, then I have earned interest of 125 per cent in the two-month period. The monthly interest, however, is 50 per cent, not 62.5 per cent, since my investment is comparable to one with a 50 per cent monthly return during two months. Methods for compounding use concepts of net present value and internal rate of return as described in Annex 1.

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Historically, all interest was considered usury

Savings groups will change local cultures

Among others, David Graeber has shown how, historically, all interest was considered usury and has argued that promoting interest rate-bearing loans might lead to social problems (Graeber, 2011). In contrast, other anthropological studies of indigenous rotating savings and credit associations have found that interest rates are a natural part of the way these groups work (Ardener and Burman, 1995). While the discussion for and against interest rates as such is relevant to microfinance as a whole, I will not go further into the discussion here. Interest rates and the reporting of interest rates are a part of current savings group practice. What I will discuss is how to report interest rates. To frame the discussion, it is useful to ask Robert Chambers’ rhetorical question: whose reality counts? Clearly, participants’ reality ultimately counts and therefore local understanding of interest is relevant. Shipton (2010) notes that few African languages have words for interest or usury and thus the very concept often lacks an indigenous counterpart. Where there are concepts similar to interest, they relate to ratios, not to rates. Indeed this is probably why flat-rate interest is so common in microfinance: it is locally accepted. Any development intervention is an ongoing negotiation of concepts and the very implementation of savings groups is an example of this negotiation. It resonates with indigenous financial arrangements, while at the same time explicitly aiming to augment these. No matter what, savings groups will change local cultures. The way interest rates are computed is a part of this change and it should be clear how and why they are calculated the way they are. Neither international standards nor local customs are in and of themselves good reasons for adopting one calculation over the other. Here the key advantage of the financial method is the ability to compare monthly and annual rates as well as rates of different providers. Few savers in Europe would be able to re-calculate the interest they get on their savings account, since it is done exactly following the methods in Annex 1. Only 18 per cent of adult Britons answered correctly when asked a simple question on compounded interest (Lusardi and Mitchell, 2007: 216). They rely on legislation and public oversight to ensure correct calculations. It seems illogical that the absence of these mechanisms should be a reason for computing and communicating incomparable interest rates, if comparison is indeed needed. In the following, I will expand on the reasons why it might be useful. In semi-mature microfinance markets such as Cambodia or Kenya, savings groups exist alongside conventional finance. Here a direct benefit is that participants are able to compare the services of the savings group with those of ordinary providers. There are many reasons for members to choose their savings groups, but Collins et al. (2009) have documented how interest rates are at least one of the

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Comparable interest rates will allow supervisors to separate credit and savings from loss

reasons. The ability to compare savings groups with other providers is one direct benefit to members of the financial calculation suggested here. A potential caveat is that there is homogeneity in savings and borrowing patterns inside the group. However, in a survey of 1,775 households in Northern Malawi, 54 per cent of group members indicated that they had not taken a loan during the past year, despite being members of a VSLA (village savings and loan association) throughout this period (Ksoll et al., 2012, authors’ calculations). This points to heterogeneous intra-group savings and borrowing practices. There are also indirect benefits. Project managers need to assess performance of the group to support the groups in need. One performance metric is money not accounted for in the groups. If savings are lent out at ten per cent per month, savers should in principle be able to take away ten per cent per month – that is, in principle, since many other things happen along the way. Taking this into account, comparable interest rates will allow supervisors to separate credit and savings from loss. This can only be done if the metrics are internally consistent: that is, when interest rates on savings and interest rates on loans have the same meaning within the reporting system.

Non-standard interest rate calculations So what is wrong with the typical interest rate calculations? There are two issues: first, the interest rate calculation itself; and, second, annualization of this rate for groups that are less than a year old.

Interest rate calculation The calculation used for annual interest rates in the current management information system developed by CARE, Oxfam, and CRS as well as on http://savingsgroups.com is:

Net profit / loss Returns on savings = Cumulative value of savings

(1)

In this paper, I call this the simple method. To illustrate the pitfalls of this method let’s look at two groups, assuming that we know their savings profile, i.e. when they save. Both save 1,000 shillings and end up with 1,100 after one full year. In Group A, everyone saves everything on 1 January. The members have to live without their 1,000 shillings for the entire year. Group B postpones saving until 1 December, at which time it saves 1,000 shillings. The members of Group B must get by without their 1,000 shillings for one month. On 31 December both groups have total assets of 1,100 shillings and profits of 10 per cent of their cumulative savings. The groups’ savings profiles are illustrated in Figures 1 and 2.

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1000

1000

500

500

0 January

0 April

July

Group A

October

January

Constant savings

Figure 1. Group A saves everything on 1 January

The savings profile matters greatly when we want to use the generated profits as a basis for calculation

January

April Group B

July

October

January

Constant savings

Figure 2. Group B saves everything on 1 December

Calculating interest using equation (1) above, both groups yield an interest rate on savings of 10 per cent per year. As should be clear from the two examples, however, the interest rate on savings in the groups is not the same. In Group A, members get 100 shillings in profits when they save their money for a year; and in Group B, they get the same in just one month. Clearly, Group B yields a higher interest rate. Following financial interest calculations, the annual real interest rate would be 10 per cent for Group A, but a staggering 214 per cent for Group B. The central point is that the savings profile matters greatly to the interest rate when we want to use the generated profits as a basis for calculation. To calculate the interest rate, we must assume a savings profile. For the present purpose, this raises two questions: what are the assumptions about the savings profile in equation (1) above, and what might the real savings profile be in savings groups? The assumption underlying the simple method is that the savings profile is exactly as in Group A. The only case where the formula is correct is when everything is saved at the beginning of the year and kept in (and lent out by) the group until payout at the end. Turning to the second question, Group A’s savings profile is unrealistic for savings groups simply because of the way the groups work. Savings are carried out by purchasing so-called shares in the groups, and members are strongly encouraged to buy at least one share, but internal rules prohibit them from buying more than five shares per week. Nevertheless, the exact savings profile is an empirical question which is analysed in the next section.

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Annualization The second non-standard calculation is annualization. The management information system uses the following formula for annualizing the interest rate:

If interest rates are to be consistent, then compounded interest must be taken into account

Annual interest rate = rperiod* 52 n

(2)

where rperiod is the period interest rate and n is the length of the period in weeks. This formula ignores compounded interest. Savings groups require payment of interest every month and even if only interest is paid, this corresponds to compounding. If interest rates are to be externally and internally consistent, as discussed above, then compounded interest must be taken into account. The standard formula for calculating the annualized interest from the available data would be to first calculate the weekly interest and then annualize. The formulae are:

rweek = (rperiod + I)I/n – I

(3)



rannual = (rweek + I)52 – I

(4)

Table 1 illustrates this for 13 periods, which is the number of four-week periods in a year. The initial loan amount is 100 shillings and monthly interest is 10 per cent. Each new period’s loan amount is simply the preceding period’s loan amount plus interest. The annual interest is 245 per cent, since a savings group year has 13 four-week periods. Table 1. Compounding interest Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7 Period 8 Period 9 Period 10 Period 11 Period 12 Period 13 Repayment Total interest

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Loan amount

Interest

100 110 121 133 146 161 177 195 214 236 259 285 314 345 245

10 11 12 13 15 16 18 19 21 24 26 29 31

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Data on interest rates and savings profiles As mentioned in the previous section, the savings profile is essential when calculating the interest rate. Certainly, the savings profile assumed by the formula currently used to compute interest rates is unrealistic. But what, then, is realistic? To answer that question, we must turn to data. The data I use here are collected every three months and contain information on, for example, total savings, total assets, and group age. Because of the multiple time points, the data give an indication of the savings profile. More time points would give more precise information. In effect, the data tell us about the overall interest on savings in the groups. After an overall description of the data, I compute the real interest rate using the standard financial calculation. Then, I primarily compare these calculations with three approximations: the current simple method, a calculation assuming constant weekly savings, and a variation of the simple method which is currently being rolled out. I call the latter the new simple method.

The data

Well-run groups might have different savings patterns to poorly managed groups

The initial data encompass 974 groups. The groups are observed every three months and most groups have more than one observation. To provide information on the savings profile, I need multiple data points, so I exclude the groups with less than four observations. That leaves 239 groups that have been observed during the course of at least a year. Following common practice in savings groups, the groups distribute all funds once per year at the end of a so-called cycle. After one cycle, it is common to start again with a larger initial savings contribution from all members. Since I do not have precise data on the funds involved in the distribution, I limit the analysis to one such cycle and, lacking information about any initial savings, I use only first-cycle groups. This leaves 204 groups for the analysis. One concern in this trimming exercise is that the subset of 204 groups is not representative of the larger pool of groups. Well-run groups might have different savings patterns to poorly managed groups. The well-run groups might also live longer and thus have a higher probability of entering my analysis. Because of this, the results are valid only for groups that survive more than one year. In practice, groups are usually considered independent after operating for one year, so the results can be thought of as valid for independent groups. Groups elsewhere might be different from the groups studied here, in which case the interest rate might also be different in other contexts. Comparing the simple interest rates with savingsgroups.com shows that these groups are similar to the global average in that respect.

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Before I turn to the analysis of the real savings profile, it is worth mentioning some descriptive statistics of the groups. These are listed in Table 2. For example, members buy an average of 82 shares in a period of 40 weeks, or two shares per meeting. The groups have been trained partly by field officers paid for by the project, and partly by village agents paid for by the groups themselves. The average number of loans per group during the whole cycle is 7.9, and 9.1 members or 53 per cent in each group are savers only at the time of data collection.

The median real interest rate is 62 per cent The key result is the effective interest rate calculated using standard financial calculations based on net present value and internal rates of return as explained in Annex 1. In practice, it takes into account the savings profile and the problems of the simple method mentioned in the example with Group A and Group B. Using this method, I calculate one effective interest rate per group using all four observations from each group. I assume that the rate of savings is constant between the dates on which the observations were made, but since there are four observations, the overall savings profile can be non-linear. If groups save more in the beginning and less at the end, this is taken into account. As such, this way of computing the interest rate imposes a minimum of assumptions on the savings profile given the available data. Of course, if the individual savings profiles differ from the group level average, the individual interest rates will be different. Using this method, the median annual real interest rate in the 204 groups is 62 per cent, or 3.8 per cent per four-week period. In contrast, Table 2. Descriptive statistics

Total no. Total no. of Mean SD overall  SD between SD within of groups* observations* groups** groups**

Group size at start of cycle

206  

17.7

Group size at the last data collection

153  

17.10

3.50

Average savings per member (Malawi Kwacha)

206  

6367

3671

Average profits per member (Malawi Kwanca)

206  

1801

1522

Share of women in groups

206

72.5%

23.7%

Dropouts since start of cycle

153  

1.13

2.20

No. of outstanding loans per group

206

7.9

6.8

787 840

3.00

22.6%

6.3%

3.0

6.1

* The number is sometimes lower than 206/840 due to missing observations in the original data. ** The standard deviation between groups is the standard deviation of the group averages from the overall average. A high value means a big difference from one group to another. The standard deviation within groups is the standard deviation of the individual group’s four observations from the group’s average. The two figures are only defined for measures that change over time.

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The simple method is wrong by at least 18 percentage points in more than 75% of the cases

the simple method generates a median interest rate of 29 per cent. The averages are 88 per cent for the financial method and 36 per cent for the simple method, but since there are a few high interest rates and many rates between zero and one, I consider the median to be a better descriptive measure in this case. Taking the financial method as the standard, the simple method is wrong by at least 18 percentage points in more than 75 per cent of the cases. It is within plus or minus 10 percentage points in only 8.3 per cent of the cases. Figure 3 displays the density plots of the two distributions. It is clear that the simple calculation falls systematically below the financial calculation. (In Figures 3 and 4, I remove between one and 16 outliers for the purpose of display. These are, however, included in the calculations.) This is a result of the fact that savings do not happen in the beginning of the cycle as the simple method assumes, but throughout the period. As such, the simple calculation underestimates the true interest rate. Further, the simple interest rate is less variable than the standard financial calculation. I conclude that the approximation used by the simple method misses the mark.

How should we report interest rates on savings in savings groups?

Density

The standard financial calculation requires computations that might seem difficult to implement as part of everyday savings group practice. Therefore, it is not practical for groups to change the way they calculate their own returns during share-out, since this process

Figure 3. Density plot of the two ways of computing interest rates

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An annual rate might give the false impression that it is a projection

To compare savings profiles, both age and savings have been normalized

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must be manageable by the group themselves and it is complicated by the fact that information from more than one time point is needed. To move forward, two options seem feasible. First, the next generation of the standard management information system is currently being developed and will use data from multiple observations per group, making direct financial calculation possible. Alternatively, one can assume constant savings and then compute the interest rate from one observation using the age of the group and the profits. In this case, the calculation can be done once and displayed in a table. This table can then be used for look-up of the real effective interest rate. Such a table is presented in Annex 2 for annual savings and Annex 3 for monthly savings. The latter is included since the interest rate will inevitably change during the cycle, and an annual rate might give the false impression that it is a projection. I use numbers from the table with annual interest rates. Compared with the standard financial calculation, the table is imprecise in two ways. Most importantly, it ignores the fact that some groups save more in the beginning of the cycle, while others save more at the end. This changes the effective interest rates. Moreover, the table must necessarily include discrete steps, in this case of 2.5 percentage points and four-week periods. To investigate the feasibility of the look-up table, I used it to arrive at the interest rates for all 204 groups and compared them with the financial calculation. In general terms, the look-up table is a much better approximation than the simple calculation. Where the simple calculation falls far below the financial calculation, the look-up table gives interest rates both below and above the financial calculation. As such, the median interest rate obtained using the table is 58 per cent, compared with 62 per cent using the standard financial calculation. The average is 85 per cent compared with 88 per cent. The difference between the look-up measure and the standard financial calculation falls around zero. In contrast, the difference between the simple and the financial calculation is systematically below zero. In fact, the error is 3.1 percentage points on the average, and the median of the error is 1.3 percentage points, a figure not statistically significant from zero at a 5 per cent level. For half of the 204 groups, the difference is between 1.1 and 3.7 percentage points. The density plots of all three calculations are shown in Figure 4. The reason for the match between the look-up table and the standard financial calculation is that, on average, the savings profiles are linear. To compare savings profiles, I have normalized both age and savings so that both are between zero and 100. This enables graphing of the savings profile. Five examples are given in Figure 5 and all 200 groups are graphed in Figure 6 to provide an illustration of the comparison of medians above: the fact that linear or constant savings is a good average approximation.

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Figure 4. Density plot of the three ways of computing interest rates

A new simple method In the monitoring and information system that VSL Associates is planning to launch in 2013, returns will be calculated using this metric:

Returns on average savings =

Net profit (5) Cumulative value of savings / 2

The key difference from Equation (1) is that cumulative savings is divided by two. It is easy to see that this will simply double the returns figure and, as such, make it much closer to the financial calculation. That there are still important differences can be seen by using the examples from Group A and Group B above: even with the new figure, these two groups will have the same interest rate because the savings profile is not taken into account. Averaging out savings assumes that early and late savings count the same. In the financial calculation, they do not and, therefore, the new simple method is systematically biased downwards. On average, in the 204 Malawian groups, the new simple calculation falls 16.2 percentage points below the financial calculation.

Even with the adjustment to the interest rate on savings, there is still an important unexplained fact

Using comparable interest rates for monitoring Even with the adjustment to the interest rate on savings obtained by the financial calculation above, there is still an important unexplained fact. The annualized interest rate on loans is 245 per cent, but the annualized interest rate on savings is 62 per cent. Where does this large difference come from? An obvious explanation is incomplete fund usage, which I analyse in the next section.

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Figure 5. Five examples of savings profiles

Figure 6. All 204 savings profiles

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Incomplete fund usage When members save in their groups, not all savings are lent out at any one time. Naturally, the funds not lent out do not accumulate interest even though they are saved. The ratio between all funds and lent-out funds is known as the loan fund use ratio. So the expected interest rate is not 245 per cent, but lower. How much lower? The interest rate on loans is set to 10 per cent or 20 per cent with a few groups higher or lower. The average is 14.9 per cent or 511 per cent annually. The average loan fund use is 46 per cent across all observations and all groups. A simple adjustment gives an annual interest rate of 230 per cent, but this figure depends on how the loan fund use ratio develops over time. The change in loan fund use is shown in Figure 7. The solid line shows the local average of loan fund use. Clearly, it is low in the beginning and at the end. At the same time, the nominal interest rate is normally constant and the savings level increases. To enable performance monitoring, I combine these three pieces of information in a ‘potential interest rate’ for each group; that is, the return on savings the groups would have made if their stated nominal interest rates and loan fund uses are correct. To arrive at this figure, I compute the loan fund used at each loan meeting by assuming that loan-fund use develops linearly between the observation points. Using total savings, I compute how potential assets would accumulate. Using the same method as described in Annex 1, I then replace the final payout

Figure 7. Loan fund use over time (locally weighted scatterplot smoothing (lowess) plot)

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The difference between the effective and potential interest rates is an excellent metric to track performance of the groups

in the sequence of payments with the potential assets and re-compute the effective interest rate. This figure is the potential interest rate. Using this information, the average potential interest rate is 109 per cent, which is considerably lower than the 230 per cent from above. Nevertheless, the calculation does not change the basic finding that some funds are missing, since there is still a gap of 47 percentage points between 62 per cent and 109 per cent. In fact, the difference between the effective interest rate and the potential interest rate, which I call the missing interest rate, is an excellent metric to track performance of the groups because it measures missing money in the groups. Project managers should visit the groups with a missing interest rate of more than, say, 20 percentage points. In the present dataset this means that 168 groups should be checked. The global data looks somewhat similar. Here I have only the simple average loan fund use, which is 52.2 per cent. Assuming a 10 per cent nominal interest rate per four-week period, the corresponding annual interest rate is 110 per cent, but taking changing loan fund use into account might reduce this. Moreover, the reported interest rate on savings of 35 per cent might be twice as high. Owing to the lack of information, it is not possible to confirm that the missing interest rate is lower than in my sample, but on the other hand it cannot be ruled out. Explaining this gap is not the purpose of the present paper and is likely to require more detailed information (e.g. from the passbooks used by many savings groups), but four possibilities seem particularly likely. First, there might be a large share of non-performing loans in the groups. Write-off of these loans is supposed to be reported, but for the 204 groups in my analysis, only one reported any write-off at all. It is possible that the groups have not yet given up on the loans, but they have not been paid back. Second, groups might have very relaxed repayment schedules without charging additional interest. Flexibility might very well be an advantage of savings groups, but this would lower the interest rate accordingly. Third, the surplus might simply have been stolen, and, finally, there might be issues of data quality. Which of these explanations is the correct one is an area for future research and will require new data, for example data from passbooks.

Conclusions

Groups offer net savers very high interest rates

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It is clear from the above treatment of interest rates in savings groups that these groups offer net savers very high interest rates, and are more beneficial to their members – primarily women – than has been previously reported. Looking at more than 200 groups in Malawi with a membership of 72.5 per cent women, I find a median interest rate of 62 per cent and a mean of 88 per cent, or monthly returns

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For once, the world’s most marginalized and poorest people are getting the world’s best deals

A high-yielding savings product needs serious assessment

between 3.8 per cent and 5.0 per cent. Data from elsewhere in Malawi show that more than half might be net savers. The officially reported figures had a median of 29 per cent and a mean of 36 per cent. If net savers are among the poorest, this is very good news. For once, the world’s most marginalized and poorest people are getting the world’s best deals. I have argued that comparable metrics are relevant even if local approaches to calculating interest do not include compounding. On the contrary, the rapid growth of credit-led microfinance makes the possibility of comparison even more important for members as well as policy-makers. Using the standard financial calculation is a prerequisite for comparison. Acknowledging that current computing power in savings group implementation is probably limited, I offer an alternative approach to calculating all interest rates: a look-up table with translations from the simple interest rate in current use to the financial calculation. This method is considerably closer to the real financial calculation. On the basis of this interest rate, I suggest a metric for monitoring group performance – the missing interest rate – which compares the interest rate on loans with the interest rate on savings. In practice, these results will matter to policy-makers, donors, and practitioners in aid. First, practitioners should acknowledge that interest rates computed using standard financial calculations are the proper way to summarize the price or yield of money in time. As already mentioned, there are signs that a tool with improved metrics will be available in 2013. The present analysis justifies adopting this revised tool because it is superior to the old one. Adapting the standard financial calculation or the suggested look-up table would, however, be better still, and would enable practitioners to assess group performance by comparing interest on loans with interest on savings to obtain the ‘missing interest’. Second, donors should sustain their funding for savings groups. Returns of 60 per cent should not be ignored. Even if the upcoming impact studies of savings groups show no effect, donors should fund studies of longer duration and greater statistical power using knowledge of how groups work gained from the first impact assessments. A high-yielding savings product needs serious assessment. Third, the comparison of interest rates on loans and savings enables calculation of the missing interest rate which, in turn, can be used to identify groups where money disappears. Everybody involved in savings groups should have an interest in finding out where missing funds go. Finally, an obvious question for future research is to look at factors that drive the effective interest rate. After having been hidden for a long time, savings groups have started to appear on the radar of policy-makers and academics. This is good news for everyone saving in, or working with, a savings group. But it will necessarily lead to comparison of savings groups and other

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314 O.D. RASMUSSEN

financial instruments and will thus require practitioners to report key metrics, such as interest rates, in ways comparable to other products in the financial landscape. Only by doing that will savings groups appear on the radar as a viable alternative or cost-effective supplement to formal financial access.

References Allen, H. and Panetta, D. (2010) Savings Groups: What Are They? Washington, DC: SEEP Network. Ardener, S. and Burman, S. (eds) (1995) Money-Go-Rounds, Oxford: Berg. Brown, R.L. and Zima, P. (2011) Mathematics of Finance, 2nd edn, New York: McGraw-Hill. Collins, D., Morduch, J., Rutherford, S. and Ruthven, O. (2009) Portfolios of the Poor: How the World’s Poor Live on $2 a Day, Washington, DC: Princeton University Press. De Mel, S., McKenzie, D. and Woodruff, C. (2008) ‘Returns to capital in microenterprises: Evidence from a field experiment’, The Quarterly Journal of Economics 123: 1329. EU Directive 2008/48/EC of the European Parliament and of the Council of 23 April 2008 on credit agreements for consumers and repealing Council Directive 87/102/EEC. Graeber, D. (2011) Debt: The First 5,000 Years, New York: Melville House Publishing. Homer, S. and Sylla, R.E. (1996) A History of Interest Rates, New Brunswick: Rutgers University Press. Ksoll, C., Lilleør, H.B., Lønborg, J.H. and O. D. Rasmussen (2012) ‘The impact of community-managed microfinance in rural Malawi: Evidence from a cluster randomized control trial’, presented at the NOVAFRICA Conference, Lisbon, 7–8 September. Lusardi, A. and Mitchell, O.S. (2007) ‘Baby Boomer retirement security: The roles of planning, financial literacy, and housing wealth’, Journal of Monetary Economics 54: 205–24 . MFTransparency (2011) Excel tool: Calculating Transparent Prices v2.10, Washington, DC: MF Transparency. Rhyne, E. and Rippey, P. (2011) ‘Crossfire: Formal vs. informal sector savings’, Enterprise Development & Microfinance 22: 87–90 . Shipton, P.M.D. (2010) Credit between Cultures: Farmers, Financiers, and Misunderstanding in Africa, New Haven, CT: Yale University Press. The Economist (2011) ‘Small wonder: A new model of microfinance for the very poor is spreading’, The Economist, 10 December 2011. Truth in Savings Act (1991) FDIC Improvement Act of 1991, Subtitle F – Truth in Savings.

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CALCULATING INTEREST RATES IN MICROFINANCE 315



Annex 1 How is the standard financial calculation different? The financial calculation used computes effective interest using net present value, which is the sum of all payments discounted to the present. The effective interest rate is the interest rate where the net present value is zero. This method is used in financial textbooks as well as mandated by financial legislators around the world. It is also recommended by Microfinance Transparency, an organization working for transparent interest rates. Annualization is done using standard compounded interest. For VSLAs, it makes sense to use weeks as the smallest period. Then the formula is:

NPV =

∑

N n = 0 (I

Cn

+ r )n

= 0

(A1)

where NPV is net present value, N is the total number of weeks and Cn is the payment in period n. For savings, this is a negative number. In period N, i.e. the period when the group is observed, this is a positive figure indicating how much the group could share out today. I find the weekly interest, r, by calculating a sequence of payments for each group, assuming that the sequence is linear between the individual observations and between the group start and the first observation. Since all groups are in their first cycle, they must have started with zero savings.

Calculation example I use the values for assets and total savings. Assets are all savings and net accumulated earnings in the group. In the second and subsequent cycles, it is common for groups to contribute a large amount at the first savings meeting, in which case the calculations below would not be valid. In my calculations, I have disregarded groups in their second cycle (this only concerned two groups). I calculate the savings per period and the average savings per week. The latter might vary over the total period. One unexplained fact for the group in the example below is the difference between assets and total savings in week one. I interpret this as a gift and thus do not count it as initial savings. The payout is total assets in the last period. Table A1 shows numbers from one group as an example.

Simple calculation Interest rate (37 weeks) =

Assets − Total savings 58650 = = 26.7% Total savings 219500

52 Interest rate (annualized) = 26.7% * = 36.6% 37

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(A2)

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316 O.D. RASMUSSEN

Table A1. Example of information used to calculate the effective interest rate Weeks in Assets Debt Total  Savings Week Savings Payout cycle savings difference difference difference per week 1

16,750 13,000 13,000

14 104,700 89,600 76,600

13

5,892

25

145,000 124,600 35,000

11

3,182

38

278,150 219,500 94,900

13

7,300 278,150

Financial calculation From the above values, I make the sequence of payments as displayed in Table A2. I then calculate the weekly interest rate using the NPV-formula above. This can be done in Excel using the functions ‘internal rate of return’ or ‘goal seek’. In my case, I use the statistical software Stata. All methods give the same results.

Interest rate (weekly) = 0.01191



Interest rate (37 weeks) = (1+0.01191)37 – 1 = 55.0%



Interest rate (annualized) = (1+0.01191)52 – 1 = 85.1%

(A3)

Table A2. Calculation of effective interest rate setting net present value to zero Period

Payment Discounted  Period Payment Discounted  Period Payment Discounted sequence value (continued) sequence value (continued) sequence value

0

–13,000

–13,000

13

–5,892

–5,051

26

–7,300

–5,365

1

–5,892

–5,823

14

–3,182

–2,696

27

–7,300

–5,302

2

–5,892

–5,754

15

–3,182

–2,664

28

–7,300

–5,240

3

–5,892

–5,687

16

–3,182

–2,633

29

–7,300

–5,178

4

–5,892

–5,620

17

–3,182

–2,602

30

–7,300

–5,117

5

–5,892

–5,553

18

–3,182

–2,571

31

–7,300

–5,057

6

–5,892

–5,488

19

–3,182

–2,541

32

–7,300

–4,997

7

–5,892

–5,423

20

–3,182

–2,511

33

–7,300

–4,938

8

–5,892

–5,360

21

–3,182

–2,481

34

–7,300

–4,880

9

–5,892

–5,297

22

–3,182

–2,452

35

–7,300

–4,823

10

–5,892

–5,234

23

–3,182

–2,423

36

–7,300

–4,766

11

–5,892

–5,173

24

–3,182

–2,395

37

–7,300

–4,710

12

–5,892

–5,112

25

–7,300

–5,429

38

278,150

177,342

Sum of all discounted values (net present value)

0

Sum of all savings (all negative values)  

–219,500

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CALCULATING INTEREST RATES IN MICROFINANCE 317



Annex 2 Determining the annual interest rate using the simple return on savings and the age of the group Using data from the group, one can look up the group’s simple returns on savings and its age within the current cycle. The corresponding cell gives the effective annualized interest rate (%) resulting from standard financial calculations. Age of group this cycle

Simple return on savings

52 48 44 40 36 32 28 24 20 16 12 8 4 0.0% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5% 4.9 5.4 5.8 6.4 7.2 8.1 9.2 10.8 12.9 16.2 21.7 32.9 66.9 5.0% 10.0 10.8 11.8 13.1 14.6 16.5 19.0 22.3 27.1 34.5 47.3 75.1 174.5 7.5% 15.1 16.4 18.0 19.9 22.2 25.3 29.2 34.6 42.5 54.9 77.3 128.8 345.1 10.0% 20.2 22.0 24.2 26.9 30.2 34.4 40.0 47.8 59.2 77.7 112.1 196.7 612.3 12.5% 25.5 27.8 30.6 34.1 38.4 44.0 51.4 61.8 77.4 103.0 152.6 282.0 1025.7 15.0% 30.8 33.7 37.2 41.5 46.9 53.9 63.3 76.7 96.9 131.1 199.3 388.4 1657.9 17.5% 36.1 39.6 43.8 49.0 55.6 64.2 75.8 92.5 118.1 162.1 253.0 520.5 2614.0 20.0% 41.6 45.7 50.6 56.8 64.6 74.8 88.9 109.2 140.8 196.4 314.6 683.3 4045.1 22.5% 47.1 51.8 57.5 64.7 73.8 85.9 102.5 126.8 165.2 234.0 384.9 883.0 6165.6 25.0% 52.6 58.0 64.6 72.8 83.3 97.4 116.8 145.5 191.4 275.2 464.8 1126.7 9277.9 27.5% 58.3 64.3 71.8 81.1 93.1 109.2 131.7 165.1 219.4 320.3 555.5 1422.5 13804.5 30.0% 64.0 70.7 79.1 89.6 103.2 121.4 147.2 185.8 249.4 369.6 658.0 1780.1 20331.0 32.5% 69.7 77.2 86.5 98.2 113.5 134.1 163.3 207.6 281.3 423.2 773.6 2210.2 29662.8 35.0% 75.5 83.8 94.0 107.0 124.0 147.1 180.0 230.4 315.3 481.5 903.4 2725.3 42899.6 37.5% 81.4 90.5 101.7 116.0 134.8 160.5 197.4 254.3 351.4 544.8 1048.9 3339.9 61532.7 40.0% 87.3 97.2 109.5 125.2 145.9 174.4 215.5 279.4 389.7 613.3 1211.6 4070.0 87570.0 42.5% 93.3 104.0 117.4 134.6 157.3 188.6 234.2 305.7 430.4 687.3 1393.0 4934.3 123698.7 45.0% 99.3 110.9 125.4 144.1 168.9 203.2 253.6 333.1 473.4 767.1 1594.8 5953.6 173491.6 47.5% 105.4 117.9 133.6 153.8 180.7 218.3 273.6 361.8 518.9 853.1 1818.7 7151.5 241671.8 50.0% 111.6 125.0 141.8 163.6 192.8 233.7 294.3 391.6 567.0 945.6 2066.7 8554.7 334446.8 52.5% 117.8 132.1 150.2 173.6 205.2 249.6 315.8 422.8 617.7 1044.8 2340.8 10193.0 459930.3 55.0% 124.0 139.3 158.6 183.8 217.9 265.9 337.9 455.2 671.1 1151.3 2643.0 12099.8 628671.7 57.5% 130.3 146.6 167.2 194.2 230.7 282.6 360.7 489.0 727.3 1265.2 2975.7 14312.7 854317.1 60.0% 136.6 153.9 175.9 204.7 243.9 299.7 384.2 524.1 786.4 1387.1 3341.1 16873.2 1154431.4 62.5% 143.0 161.3 184.7 215.4 257.3 317.2 408.5 560.5 848.5 1517.2 3741.8 19828.0 1551516.8 65.0% 149.5 168.8 193.6 226.3 270.9 335.1 433.5 598.4 913.7 1655.9 4180.5 23228.4 2074271.5 67.5% 155.9 176.4 202.6 237.3 284.9 353.5 459.2 637.6 982.0 1803.6 4659.9 27131.7 2759127.0 70.0% 162.5 184.1 211.8 248.5 299.0 372.2 485.6 678.3 1053.6 1960.8 5182.9 31601.1 3652144.9 72.5% 169.0 191.8 221.0 259.8 313.5 391.4 512.8 720.4 1128.4 2127.9 5752.6 36706.4 4811312.6 75.0% 175.7 199.5 230.3 271.3 328.1 411.1 540.8 764.0 1206.8 2305.2 6372.2 42524.4 6309347.1 77.5% 182.3 207.4 239.7 283.0 343.1 431.1 569.5 809.2 1288.6 2493.2 7045.2 49139.8 8237085.5 80.0% 189.0 215.3 249.3 294.8 358.2 451.6 598.9 855.8 1374.0 2692.3 7775.0 56645.6 10707567.3 82.5% 195.8 223.2 258.9 306.8 373.7 472.5 629.2 904.1 1463.2 2903.1 8565.4 65143.5 13860963.2 85.0% 202.6 231.3 268.6 318.9 389.4 493.8 660.2 953.8 1556.1 3125.8 9420.2 74745.1 17870472.4 87.5% 209.4 239.4 278.5 331.2 405.3 515.5 692.0 1005.2 1652.9 3361.2 10343.6 85572.2 22949383.5 90.0% 216.3 247.5 288.4 343.6 421.5 537.7 724.6 1058.2 1753.7 3609.5 11339.8 97758.0 29359475.3 92.5% 223.2 255.8 298.4 356.2 437.9 560.3 758.0 1112.9 1858.5 3871.3 12413.1 111447.2 37421052.6 95.0% 230.1 264.1 308.5 368.9 454.6 583.3 792.2 1169.2 1967.5 4147.1 13568.3 126797.7 47524724.3 97.5% 237.1 272.4 318.8 381.8 471.6 606.8 827.1 1227.3 2080.8 4437.4 14810.1 143981.0 60145533.2 100.0% 244.1 280.8 329.1 394.9 488.7 630.7 862.9 1287.0 2198.4 4742.8 16143.5 163182.9 75859401.6

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318 O.D. RASMUSSEN

Annex 3 Determining the monthly interest rate using the simple return on savings and the age of the group Using data from the group, one can look up the group’s simple returns on savings and its age within the current cycle. The corresponding cell gives the effective monthly interest rate (%) resulting from standard financial calculations. Age of group this cycle

Simple return on savings

52 48 44 40 36 32 28 24 20 16 12 8 4 0.0% 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.5% 0.4 0.4 0.4 0.5 0.5 0.6 0.7 0.8 0.9 1.2 1.5 2.2 4.0 5.0% 0.7 0.8 0.9 0.9 1.1 1.2 1.3 1.6 1.9 2.3 3.0 4.4 8.1 7.5% 1.1 1.2 1.3 1.4 1.6 1.7 2.0 2.3 2.8 3.4 4.5 6.6 12.2 10.0% 1.4 1.5 1.7 1.8 2.1 2.3 2.6 3.1 3.6 4.5 6.0 8.7 16.3 12.5% 1.8 1.9 2.1 2.3 2.5 2.8 3.2 3.8 4.5 5.6 7.4 10.9 20.5 15.0% 2.1 2.3 2.5 2.7 3.0 3.4 3.8 4.5 5.4 6.7 8.8 13.0 24.7 17.5% 2.4 2.6 2.8 3.1 3.5 3.9 4.4 5.2 6.2 7.7 10.2 15.1 28.9 20.0% 2.7 2.9 3.2 3.5 3.9 4.4 5.0 5.8 7.0 8.7 11.6 17.2 33.2 22.5% 3.0 3.3 3.6 3.9 4.3 4.9 5.6 6.5 7.8 9.7 12.9 19.2 37.5 25.0% 3.3 3.6 3.9 4.3 4.8 5.4 6.1 7.2 8.6 10.7 14.2 21.3 41.8 27.5% 3.6 3.9 4.2 4.7 5.2 5.8 6.7 7.8 9.3 11.7 15.6 23.3 46.2 30.0% 3.9 4.2 4.6 5.0 5.6 6.3 7.2 8.4 10.1 12.6 16.9 25.3 50.6 32.5% 4.2 4.5 4.9 5.4 6.0 6.8 7.7 9.0 10.8 13.6 18.1 27.3 55.0 35.0% 4.4 4.8 5.2 5.8 6.4 7.2 8.2 9.6 11.6 14.5 19.4 29.3 59.4 37.5% 4.7 5.1 5.5 6.1 6.8 7.6 8.7 10.2 12.3 15.4 20.7 31.3 63.9 40.0% 4.9 5.4 5.9 6.4 7.2 8.1 9.2 10.8 13.0 16.3 21.9 33.2 68.4 42.5% 5.2 5.6 6.2 6.8 7.5 8.5 9.7 11.4 13.7 17.2 23.1 35.2 72.9 45.0% 5.4 5.9 6.5 7.1 7.9 8.9 10.2 11.9 14.4 18.1 24.3 37.1 77.5 47.5% 5.7 6.2 6.7 7.4 8.3 9.3 10.7 12.5 15.1 18.9 25.5 39.0 82.1 50.0% 5.9 6.4 7.0 7.7 8.6 9.7 11.1 13.0 15.7 19.8 26.7 40.9 86.7 52.5% 6.2 6.7 7.3 8.1 9.0 10.1 11.6 13.6 16.4 20.6 27.9 42.8 91.3 55.0% 6.4 6.9 7.6 8.4 9.3 10.5 12.0 14.1 17.0 21.5 29.0 44.7 96.0 57.5% 6.6 7.2 7.9 8.7 9.6 10.9 12.5 14.6 17.6 22.3 30.2 46.6 100.6 60.0% 6.9 7.4 8.1 8.9 10.0 11.2 12.9 15.1 18.3 23.1 31.3 48.4 105.3 62.5% 7.1 7.7 8.4 9.2 10.3 11.6 13.3 15.6 18.9 23.9 32.4 50.3 110.1 65.0% 7.3 7.9 8.6 9.5 10.6 12.0 13.7 16.1 19.5 24.7 33.5 52.1 114.8 67.5% 7.5 8.1 8.9 9.8 10.9 12.3 14.2 16.6 20.1 25.4 34.6 53.9 119.6 70.0% 7.7 8.4 9.1 10.1 11.2 12.7 14.6 17.1 20.7 26.2 35. 55.7 124.4 72.5% 7.9 8.6 9.4 10.4 11.5 13.0 15.0 17.6 21.3 27.0 36.8 57.5 129.2 75.0% 8.1 8.8 9.6 10.6 11.8 13.4 15.4 18.0 21.9 27.7 37.8 59.3 134.0 77.5% 8.3 9.0 9.9 10.9 12.1 13.7 15.7 18.5 22.4 28.5 38.9 61.1 138.9 80.0% 8.5 9.2 10.1 11.1 12.4 14.0 16.1 19.0 23.0 29.2 39.9 62.9 143.7 82.5% 8.7 9.4 10.3 11.4 12.7 14.4 16.5 19.4 23.6 29.9 40.9 64.6 148.6 85.0% 8.9 9.7 10.6 11.6 13.0 14.7 16.9 19.9 24.1 30.6 42.0 66.4 153.5 87.5% 9.1 9.9 10.8 11.9 13.3 15.0 17.3 20.3 24.6 31.3 43.0 68.1 158.4 90.0% 9.3 10.1 11.0 12.1 13.5 15.3 17.6 20.7 25.2 32.0 44.0 69.8 163.4 92.5% 9.4 10.3 11.2 12.4 13.8 15.6 18.0 21.2 25.7 32.7 45.0 71.6 168.3 95.0% 9.6 10.5 11.4 12.6 14.1 15.9 18.3 21.6 26.2 33.4 46.0 73.3 173.3 97.5% 9.8 10.6 11.6 12.9 14.3 16.2 18.7 22.0 26.8 34.1 47.0 75.0 178.3 100.0% 10.0 10.8 11.9 13.1 14.6 16.5 19.0 22.4 27.3 34.8 47.9 76.7 183.3

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